Robert J Aumann
Biographic Data
| ID | 931851 |
|---|---|
| NAME | Robert J Aumann |
| GIVEN NAMES | Robert J |
| FAMILY NAME | Aumann |
| SIGNATURE | AUMANN R J |
| AFFILIATIONS | Hebrew University of Jerusalem |
| ORCID | 0000-0001-7841-3719 |
| VERIFIED | Yes |
| TOTAL WORKS | 14 |
| TOTAL CITATIONS | 6 |
| WORKS AS AUTHOR | 14 |
| WORKS AS EDITOR | 0 |
| FIRST PUBLICATION YEAR | 1959 |
| LATEST PUBLICATION YEAR | 2023 |
| H-INDEX | 2 |
The World of Game Theory and Game Theory of the World
Ceci est le texte de l’intervention de l’auteur au colloque organisé en son honneur le 11 octobre 2021 à l’Université Paris-Panthéon-Assas, à l’occasion de la réception le lendemain d’un doctorat honoris causa décerné par cette même université. Après avoir remercié les initiateurs et les organisateurs de l’événement, et rendu hommage aux grandes figures disparues de la théorie des jeux, l’auteur décrit son « parcours personnel » dans la science. …
A synthesis of behavioural and mainstream economics
An Economic Index of Riskiness
Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a “duality ” axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dom…
Epistemic Conditions for Nash Equilibrium
Handbook of Game Theory
Journal Article Handbook of Game Theory: With Economic Applications, Volume I Get access Handbook of Game Theory: With Economic Applications, Volume 1. Edited by (Robert J.) Aumann and Hart (Sergiu). (Amsterdam, New York and Oxford: North-Holland, 1992. Pp. xxvi + 733. Dfl. 250.00 hardback, US $87.50 hardback. ISBN 0 444 88098 4.) Hal R. Varian Hal R. Varian University of Michigan Search for other works by this author on: Oxford Academic Google S…
Correlated Equilibrium as an Expression of Bayesian Rationality
If it is common knowledge that the players in a game are Bayesian utility maximizers who treat uncertainty about other players' actions like any other uncertainty, then the outcome is necessarily a correlated equilibrium. Random strategies appear as an expression of each player's uncertainty about what the others will do, not as the result of willful randomization. Use is made of the common prior assumption, according to which differences in prob…
Game theoretic analysis of a bankruptcy problem from the Talmud
Agreeing to Disagree
Two people, 1 and 2, are said to have common knowledge of an event $E$ if both know it, 1 knows that 2 knows it, 2 knows that 1 knows is, 1 knows that 2 knows that 1 knows it, and so on. THEOREM. If two people have the same priors, and their posteriors for an event $A$ are common knowledge, then these posteriors are equal.
Subjectivity and correlation in randomized strategies
Markets with a Continuum of Traders
It is suggested that the most natural mathematical model for a market with perfect competition is one in which there is a continuum of traders (like the continuum of points on a line). It is shown that the core of such a market coincides with the set of its allocations, i.e., allocations which constitute a competitive equilibrium when combined with an appropriate price structure.
A Definition of Subjective Probability
Utility Theory without the Completeness Axiom
Some theorems concerning the existence of continuous utility functions for closed preorders on submetrizable hemicompact kspaces are proved.These spaces are precisely the inductive limits of increasing sequences of metric compact subspaces and in general are neither metrizable nor locally compact.These results generalize some well known theorems due to Levin.
The Game of Politics
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Acceptable Points in General Cooperative n-Person Games
In this paper, we introduce a new theory for n-person games. Like many previous theories for n-person games, it is based on the search for a reasonable ‘‘steady state’ ’ in the ‘‘supergame,’’1 i.e., the game each play of which consists of a long sequence of plays of the original game. We use
The Game of Politics
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
An Economic Index of Riskiness
Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a “duality ” axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dom…
A synthesis of behavioural and mainstream economics
Acceptable Points in General Cooperative n-Person Games
In this paper, we introduce a new theory for n-person games. Like many previous theories for n-person games, it is based on the search for a reasonable ‘‘steady state’ ’ in the ‘‘supergame,’’1 i.e., the game each play of which consists of a long sequence of plays of the original game. We use
Utility Theory without the Completeness Axiom
Some theorems concerning the existence of continuous utility functions for closed preorders on submetrizable hemicompact kspaces are proved.These spaces are precisely the inductive limits of increasing sequences of metric compact subspaces and in general are neither metrizable nor locally compact.These results generalize some well known theorems due to Levin.
The Game of Politics
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
A Definition of Subjective Probability
Markets with a Continuum of Traders
It is suggested that the most natural mathematical model for a market with perfect competition is one in which there is a continuum of traders (like the continuum of points on a line). It is shown that the core of such a market coincides with the set of its allocations, i.e., allocations which constitute a competitive equilibrium when combined with an appropriate price structure.
Subjectivity and correlation in randomized strategies
Agreeing to Disagree
Two people, 1 and 2, are said to have common knowledge of an event $E$ if both know it, 1 knows that 2 knows it, 2 knows that 1 knows is, 1 knows that 2 knows that 1 knows it, and so on. THEOREM. If two people have the same priors, and their posteriors for an event $A$ are common knowledge, then these posteriors are equal.
Game theoretic analysis of a bankruptcy problem from the Talmud
Correlated Equilibrium as an Expression of Bayesian Rationality
If it is common knowledge that the players in a game are Bayesian utility maximizers who treat uncertainty about other players' actions like any other uncertainty, then the outcome is necessarily a correlated equilibrium. Random strategies appear as an expression of each player's uncertainty about what the others will do, not as the result of willful randomization. Use is made of the common prior assumption, according to which differences in prob…
Handbook of Game Theory
Journal Article Handbook of Game Theory: With Economic Applications, Volume I Get access Handbook of Game Theory: With Economic Applications, Volume 1. Edited by (Robert J.) Aumann and Hart (Sergiu). (Amsterdam, New York and Oxford: North-Holland, 1992. Pp. xxvi + 733. Dfl. 250.00 hardback, US $87.50 hardback. ISBN 0 444 88098 4.) Hal R. Varian Hal R. Varian University of Michigan Search for other works by this author on: Oxford Academic Google S…
Epistemic Conditions for Nash Equilibrium
An Economic Index of Riskiness
Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a “duality ” axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dom…
A synthesis of behavioural and mainstream economics
The World of Game Theory and Game Theory of the World
Ceci est le texte de l’intervention de l’auteur au colloque organisé en son honneur le 11 octobre 2021 à l’Université Paris-Panthéon-Assas, à l’occasion de la réception le lendemain d’un doctorat honoris causa décerné par cette même université. Après avoir remercié les initiateurs et les organisateurs de l’événement, et rendu hommage aux grandes figures disparues de la théorie des jeux, l’auteur décrit son « parcours personnel » dans la science. …
Mathematics (10 works) · Mathematical economics (9 works) · Computer Science (7 works) · Economics (7 works) · Game Theory and Applications (7 works) · Economic theories and models (4 works) · Economic Theory and Institutions (4 works) · Philosophy (4 works) · Econometrics (3 works) · Game theory (3 works)